Madhava of Sangamagrama, an Indian mathematician and astronomer, is widely recognized for his discovery of the infinite series expansion for the sine function.

The series expansion discovered by Madhava for the sine function is known as the Madhava Series.

The general formula for the Madhava Series expansion of the sine function is $sin(x) = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + ...$

The Madhava Series expansion has several significant implications in trigonometry, including providing accurate approximations, enabling table-free calculations, and facilitating the derivation of other trigonometric identities and formulas.

Madhava of Sangamagrama is credited with discovering the Half-Angle Formulas in trigonometry.

The general formula for the Half-Angle Formula for sine is $sin(\frac{x}{2}) = \sqrt{\frac{1 - cos(x)}{2}}$.

The general formula for the Half-Angle Formula for cosine is $cos(\frac{x}{2}) = \sqrt{\frac{1 + cos(x)}{2}}$.

Madhava's contributions to trigonometry, particularly his discovery of the Madhava Series and the Half-Angle Formulas, laid the groundwork for the development of calculus.

Madhava of Sangamagrama is regarded as the founder of the Kerala School of Astronomy and Mathematics, which made significant contributions to mathematics and astronomy in medieval India.

Madhava of Sangamagrama authored the astronomical treatise titled 'Yuktibhasa', which contains his mathematical and astronomical findings.

Madhava's work in trigonometry was largely centered around the concept of infinite series expansions, particularly the Madhava Series for the sine function.

Madhava's contributions to trigonometry primarily influenced mathematical developments within India, particularly in the Kerala School of Astronomy and Mathematics.

Madhava's infinite series expansion was primarily developed for the sine function.

Madhava's contributions to trigonometry have far-reaching significance, including laying the groundwork for calculus, providing accurate approximations, and enabling the derivation of trigonometric identities.